Abstract
We report the transverse single-spin asymmetries of $J/\psi$ production at forward and backward rapidity, $1.2<|y|<2.2$, as a function of $J/\psi$ transverse momentum ($p_T$) and Feynman-$x$ ($x_F$). The data analyzed were recorded by the PHENIX experiment at the Relativistic Heavy Ion Collider in 2015 from $p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions with transversely polarized proton beams at $\sqrt{s_{_{NN}}}=200$ GeV. At this collision energy, single-spin asymmetries for heavy-flavor particle production of $p$$+$$p$ collisions provide access to the spin-dependent gluon distribution and higher-twist correlation functions inside the nucleon, such as the gluon Qiu-Sterman and trigluon correlation functions. Proton+nucleus collisions offer an excellent opportunity to study nuclear effects on the correlation functions. The data indicate negative asymmetries at the two-standard-deviation level in the $p$$+$Au data for $p_T<2$ GeV/$c$ at both forward and backward rapidity, while in $p$$+$$p$ and $p$$+$Al collisions the asymmetries are consistent with zero within the range of experimental uncertainties.
Highlights
In polarized p þ p collisions, the transverse single spin asymmetry (TSSA), AN, is defined as the amplitude of the azimuthal angular modulation of the outgoing particle’s scattering cross section with respect to the transverse spin direction of the polarized proton
Theoretical predictions which were purely based on perturbative calculations showed that the TSSA should be inversely proportional to the hard scale of the scattering [1], and if applied to the reactions at energies accessible at the Relativistic Heavy Ion Collider (RHIC), the asymmetry would be very small, of order 10−4
In p þ Au collisions, the asymmetry in the high-pT bin is consistent with zero, there is a trend to a nonzero AN in the low-pT bin in both the forward and backward directions
Summary
In polarized p þ p collisions, the transverse single spin asymmetry (TSSA), AN, is defined as the amplitude of the azimuthal angular modulation of the outgoing particle’s scattering cross section with respect to the transverse spin direction of the polarized proton. As it has been described above, at low pT, the nonperturbative TMD Sivers function will be responsible for its SSA, while twist-3 dominates the contributions to the SSA when pT ∼ Q. PHENIX has measured the TSSA for J=ψ production at central and forward rapidities [37] and, at small pT values, where the J=ψ mass becomes the large scale Q in TMD factorization, the result has been compared to a gluon Sivers function derived in the context of the color-evaporation model in [38] and the generalized-parton model in [39]. The new PHENIX p þ A collision data offer the opportunity to quantify how this shift in x affects the twist-3 description of the TSSA’s discussed above
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